Gaussian Optics Analysis for Human Eyes with Application for Vision Corrections

Aims: To derive formulae and analyze the roles of ocular components of human eye on the refractive power in various applications.

Study Design: Gaussian optics analysis.

Place and Duration of Study: Taipei, Taiwan, between May 2015 and August 2016.

Methodology: An effective eye model is introduced by the ocular components of human eye including refractive indexes, surface radius (r1, r2, R1, R2) and thickness (t,T) of the cornea and lens, the anterior chamber depth(S1) and the vitreous length (S2). Gaussian optics is used to calculate the change rate of refractive error per unit amount of ocular components of a human eye.

Results: For typical corneal and lens power of 42 and 21.9 diopters, the rate function defined by the change of refractive error (De) due to the change of ocular components, or Mj =dDe/dQj, with j=1 to 6 for Qj= r1, r2, R1, R2, t, T are calculated for a 1% change of Qj M1=+0.485, M2=-0.063, M3=+0.053, M4=+0.091, M5=+0.012,and M6=-0.021 diopters. For 1.0 mm increase of S1 and S2, the rate functions are: M7=+1.35, and M8=-2.67 diopter/mm.

Conclusion: Using Gaussian optics, we have derived analytic formulas for the change of refractive power due to various ocular parameter changes. These formulas provide the amount of refractive error corrections in various applications including laser in situ keratomileusis (LASIK) surgery and scleral ablation for accommodation.